The cylinder intersections visualization in teaching descriptive geometry.

Marin, Gheorghe ; Petrescu, Ligia ; Dolga, Lia 等

1. INTRODUCTION

The conception, development and illustration of technical information by means of graphical method represent an ultimate part of the engineering activity. As a result, training and developing the skill to "mentally 3D see", to imagine and create best spatial shapes for certain functions, are essential for training the future mechanical engineer.

The descriptive geometry (Biran, A.; Lopez-Pulido R. 2005) is one of the difficult common disciplines, which the first year student at mechanical faculty has to face with. For the most students the secondary school knowledge in this discipline is almost non-existent. Skills in the mentally spatial modeling of shapes, in the process of drawing these mentally modeled shapes in plan graphical views, the spatial view, are at the beginning at very various levels, from medium, seldom very developed, to non-existent or almost non-existent levels. As a subject matter in the first year, the descriptive geometry is intended to train and develop these skills.

Computer aided designing and spatial visualization systems can be successfully used in teaching descriptive geometry. However, these techniques are not conceived for didactic purpose because their use in training activity requires significant efforts.

2. ASPECTS OF CAD TECHNIQUES USED IN THE DESCRIPTIVE GEOMETRY STUDY

Using the CAD techniques implies the assimilation by students not only of the descriptive geometry but also of the methods for geometrically modeling and defining CAD features.

Nevertheless, teaching the descriptive geometry should take into consideration its essential specific purposes: improving visually geometric reasoning, training the spatial view and ability to transfer information between 2D and 3D space mutually.

Under the above mention considerations, the study of a number of bibliographical books and papers in the field, the study plans in different worldwide engineering universities and their own attempts, the authors consider as necessary the assimilation of the 3D-CAD modeling techniques before learning the descriptive geometry advanced ideas (solids representations, solids and evolutes intersections).

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Approaching the spatial modeling should naturally be preceded by good knowledge of the 2D-CAD techniques. Under these conditions, the descriptive geometry study should consist in two training stages; the first including essential elements and the second the advanced elements. The second stage comes after assimilation of the basis elements in conventional plan views and in the plan and spatial computer aided views, respectively (fig. 1).

In order to acquire efficiency in teaching the descriptive geometry, the CAD techniques should be implemented according to a strict plan based on a unitary discipline outlook and a structure, with clearly defining the purpose and modeling methods used, and creating some best working algorithms. The student should always be aware of what it is modeled, for what purpose, by which methods, what is the operations sequence, what it is essential to be noticed during the process and what he should finally obtain.

Teacher should define these elements under the specific conditions of the descriptive geometry.

The experts settle two descriptive geometry-learning strategies:

* Visual learning described by a great trust in- and an especial using of the imagination and mental visualization capacity;

* "Haptic" learning strategy based on additional tactile and moving elements and references. There is an opinion that a quarter of persons has a "haptic" learning approach and does not have quickness and intuition in the correct mental visualization of objects.

The persons natively gifted with such capability are considered to use almost exclusively the first strategy. They can easily elaborate reasoning based on mental imagines exclusively. The classic method of training in the descriptive geometry field has very good results in their case. For those individuals who resort to the "haptic" strategy using computer in the descriptive geometry learning process may be very useful.

3. THE ADVANTAGES OF USING COMPUTER FOR THE DESCRIPTIVE GEOMETRY

The total reproduction of a geometric construction requires at least two images followed by their exclusively mental combination. The CAD spatial modeling allows straight visualization in the virtual three-dimension space, model examination from different space points, using colors, selective visualization of some model parts, quickly and simply getting orthogonal views.

The classic working technique of the descriptive geometry allows graphic study of a single case. A new case means a new graphic construction. By means of computer, generalizations of the studied problem are possible by relocating and rotating some geometric elements.

The CAD techniques for solids modeling allow the combination of the simple geometric shapes in order to generate complex shapes, thus being possible to achieve intersection curves. The automat generation of any main and/or auxiliary orthogonal projections, in views and sections, with separating the visible and invisible edges, are particularly valuable facilities offered by computer.

4. GENERAL RECOMMENDATIONS FOR SOLVING PROBLEMS

In the descriptive geometry, the computer may be used in two ways: for problems 2D solving according to the manual methods, the computer replacing only the drawing tools, and for problems 3D modeling, respectively, by emphasizing 3D solutions (Ryan, D. L. 1991). Considering the large industrial application, the authors have proposed the cylinder intersections study: The oblique cylinder can be modeled in four steps, by the extrusion of a circle along a line parallel to the generatrix, followed by its upper part sectioning. Use the same method to draw the second oblique cylinder.

The study of the intersection curves of the two cylinders is based on the interference solid construction (Chao, Y. et al., 1999) and not on the Boolean operations (reunion, intersection, difference). Thus, this method allows keeping the original cylinders.

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The program compares the two solids sets and requests the option for creating the interference solid as a new object.

In order to generate composite solids by the reunion and difference of the two cylinders, apply the desired Boolean operation. The resulted composite solid can be studied by freezing all the layers excepting the study one (fig. 4).

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3. CONCLUSION

One of the main "disadvantages" of the plan views specific to the descriptive geometry is the difficulty to suggest space intuitively (Standiford, K. 2001), (Standiford, K., et al., 2001).

Using the computer in study of the descriptive geometry can be an efficient method providing a correct application. This method offers large generalization possibilities being attractive and nice at the same time. However, this progressive step requires changes in the sequence of teaching the engineering graphic disciplines, during two year of study, in two stages. The second stage comes after assimilation of the basis elements in conventional plan views and in the plan and spatial computer aided views, respectively.

4. REFERENCES

Biran, A.; Lopez-Pulido R. (2005). An Analytical introduction to Descriptive Geometry, Available from: http:// meeng.technion.ac.il/Studies/PDF_Files/Descriptive.pdf Accessed: 2008-01-15

Chao, Y.; Watanabe, T.& Minemura, K. (1999). Inferring solid objects with cylindrical surfaces from orthographicviews, Proceedings. Third International Conference on Computational Intelligence and Multimedia Applications 1999 ICCIMA '99, 1999. pp. 191-195 , ISBN 0-7695-0300-4, New Delhi, India

Standiford, K. (2001). Descriptive Geometry, Thompson Delmar Learning, ISBN 0766811239, New York, USA

Standiford, K.; Standiford, D. (2001). An Integrated Approach Using AutoCAD, Thompson Delmar Learning, ISBN 0766811239, New York, USA

Ryan, D. L. (1991). CAD/CAE Descriptive Geometry, CRC Press, ISBN 0849342732, New York, USA